Question

What is the reference angle of sec 15pi/4 ?

Answer 1

The reference angle of sec (15π/4) is π/4.

Step-by-step explanation:

The reference angle of sec (15π/4) can be found by finding the acute angle formed between the terminal side of the angle and the x-axis on the unit circle. To do this, we need to determine the equivalent angle between 0 and 2π, and then find the reference angle of that equivalent angle.

First, let's find the equivalent angle between 0 and 2π for 15π/4:

15π/4 = 2π + π/4

So, the angle with the same terminal side as sec (15π/4) in the interval 0 to 2π is π/4.

Now, let's find the reference angle of π/4. Since π/4 is in the first quadrant, the reference angle is also π/4.